- Michael Ortiz
Given three mutually tangent circles as shown, it is possible to construct a fourth circle tangent to each of them, inscribed in the circular "triangle" between them, as well as a fifth circle tangent to each and containing all. The construction is a special case of an algorithm explored by Apollonius of Perga, one of the great geometers of Greek antiquity. The same algorithm is applied to construct six new circles each tangent to three of the five original, and so on, ad infinitum. The resulting figure is known as an Apollonian net; the set of circles contained by each triangle is called an Apollonian gasket. It is an example of a non-self-similar fractal, as opposed to the more commonly known self-similar fractals, such as the Sierpinski triangle and the Koch snowflake. The relative sizes of the generating circles may be adjusted by moving the indicated point. Press the button to generate the net.